Question

Lines b and c are parallel.

Horizontal and parallel lines b and c are cut by transversal a. Where line b intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: (13 x + 9) degrees, 2, 4, 3. Where line c intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, (5 x + 9) degrees, 8.
What is the measure of Angle6?

mAngle6 = 45°
mAngle6 = 54°
mAngle6 = 117°
mAngle6 = 126°

Answer 1

126°

Reason: (13x + 9)° and (5x + 9)° are consecutive interior angles on the same side of the transversal, so they are supplementary:
(13x+9) + (5x+9) = 180 → 18x + 18 = 180 → x = 9.

Then angle6 = 180° − (5x + 9) = 180° − (45 + 9) = 180° − 54° = 126°.